Nonlinear Resource Allocation Problem Research Articles

On closed-form solutions of a resource allocation problem in parallel funding of R&D projects

In order to reduce the risk of complete failure, research managers often adopt a parallel strategy by simultaneously funding several R&D activities and several research teams within each activity. The parallel strategy requires the allocation of an available budget to a number of R&D activities, the determination of the number of research teams within each activity and the amount of funding they receive. We consider a formulation of this problem as a nonlinear resource allocation problem by Gerchak and Kilgour, IEE Trans. 31 (2) (1999) 145, and present a sufficient condition as a function of problem parameters, under which closed-form solutions to the problem are obtained.

Algorithms for Separable Nonlinear Resource Allocation Problems

We consider a simple resource allocation problem with a single resource constraint. The objective function is composed of separable, convex performance functions, one for each activity. Likewise, the constraint has separable, convex resource-usage functions, one for each activity. The objective is to minimize the sum of the performance functions, subject to satisfying the resource constraint and nonnegativity constraints. This problem extends the well-studied problem in which the resource constraint is linear. We present several algorithms to solve the problem. These algorithms extend approaches developed for the linearly constrained problem. They can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables. We provide several examples for illustration purposes, present computational results, and highlight the similarities and differences among the algorithms.

The Nonlinear Resource Allocation Problem

In this paper we study the nonlinear resource allocation problem, defined as the minimization of a convex function over one convex constraint and bounded integer variables. This problem is encountered in a variety of applications, including capacity planning in manufacturing and computer networks, production planning, capital budgeting, and stratified sampling. Despite its importance to these and other applications, the nonlinear resource allocation problem has received little attention in the literature. Therefore, we develop a branch-and-bound algorithm to solve this class of problems. First we present a general framework for solving the continuous-variable problem. Then we use this framework as the basis for our branch-and-bound method. We also develop reoptimization procedures and a heuristic that significantly improve the performance of the branch-and-bound algorithm. In addition, we show how the algorithm can be modified to solve nonconvex problems so that a concave objective function can be handled. The general algorithm is specialized for the applications mentioned above and computational results are reported for problems with up to 200 integer variables. A computational comparison with a 0, 1 linearization approach is also provided.